R. Cosset, Applications des fonctions thêta à la cryptographie sur courbes hyperelliptiques, 2011.

D. A. Cox, The arithmetic-geometric mean of Gauss, Enseign. Math, vol.30, issue.2, pp.275-330, 1984.

B. Deconinck, M. Heil, A. Bobenko, M. Van-hoeij, and M. Schmies, Computing Riemann theta functions, Mathematics of Computation, vol.73, issue.247, pp.1417-1442, 2004.
DOI : 10.1090/S0025-5718-03-01609-0

R. Dupont, Moyenne arithmético-géométrique, suites de Borchardt et applications, 2006.

R. Dupont, Fast evaluation of modular functions using Newton iterations and the AGM, Mathematics of Computation, vol.80, issue.275, pp.1823-1847, 2011.
DOI : 10.1090/S0025-5718-2011-01880-6

URL : https://hal.archives-ouvertes.fr/hal-00644845

A. Enge, The complexity of class polynomial computation via floating point approximations, Mathematics of Computation, vol.78, issue.266, pp.1089-1107, 2009.
DOI : 10.1090/S0025-5718-08-02200-X

URL : https://hal.archives-ouvertes.fr/inria-00001040

A. Enge and E. Thomé, CMH ? Computation of Igusa Class Polynomials, 2014.

A. Enge and E. Thomé, Computing Class Polynomials for Abelian Surfaces, Experimental Mathematics, vol.23, issue.2, pp.129-145, 2014.
DOI : 10.1090/S0025-5718-2013-02712-3

URL : https://hal.archives-ouvertes.fr/hal-00823745

P. Gaudry, Fast genus 2 arithmetic based on Theta functions, Journal of Mathematical Cryptology, vol.1, issue.3, pp.243-265, 2007.
DOI : 10.1515/JMC.2007.012

URL : https://hal.archives-ouvertes.fr/inria-00000625

E. Gottschling, Explizite Bestimmung der Randfl???chen des Fundamentalbereiches der Modulgruppe zweiten Grades, Mathematische Annalen, vol.83, issue.2, pp.103-124, 1959.
DOI : 10.1007/BF01342938

B. Helfrich, Algorithms to construct minkowski reduced and hermite reduced lattice bases, Theoretical Computer Science, vol.41, pp.125-139, 1985.
DOI : 10.1016/0304-3975(85)90067-2

J. Igusa, Theta functions, 1972.
DOI : 10.1007/978-3-642-65315-5

H. Klingen, Introductory lectures on Siegel modular forms, 1990.
DOI : 10.1017/CBO9780511619878

H. Labrande, Computing Jacobi???s $\theta $ in quasi-linear time, Mathematics of Computation, 2015.
DOI : 10.1090/mcom/3245

W. Luther and W. Otten, Reliable computation of elliptic functions, J.UCS, vol.4, issue.1, pp.25-33, 1998.

O. Makarov, The connection between algorithms of the fast Fourier and Hadamard transformations and the algorithms of Karatsuba, Strassen, and Winograd, USSR Computational Mathematics and Mathematical Physics, vol.15, issue.5, pp.1-11, 1975.
DOI : 10.1016/0041-5553(75)90099-3

D. Mumford, Tata lectures on Theta, volume I. Birkhäuser, 1983.

M. Streng, Computing Igusa class polynomials, Mathematics of Computation, vol.83, issue.285, p.2014
DOI : 10.1090/S0025-5718-2013-02712-3

P. Van-wamelen, Equations for the Jacobian of a hyperelliptic curve, Transactions of the American Mathematical Society, vol.350, issue.08, pp.3083-3106, 1998.
DOI : 10.1090/S0002-9947-98-02056-X